Finite-Time Singularities of Solutions of a Class of Nonlinear Schrodinger Equations

摘要

Solutions to the initial-boundary value problem for a class of nonlinear Schrodinger equations are considered. Sufficient conditions are found so that the solutions do not exist for all times t > 0. An explicit upper bound of the t interval of existence of the solutions is obtained. The time evolution of a singularity is demonstrated numerically in the case of the one-dimensional Schrodinger equation.